A strain wave gearing unit having a cup-shaped externally toothed gear is proposed in Patent Document 1. In this strain wave gearing unit, a cross roller bearing is disposed on the rear side of the cup-shaped externally toothed gear. A cylindrical unit housing is disposed so as to enclose the external periphery of the cup-shaped externally toothed gear. An internally toothed gear is integrated in the inner peripheral portion of the front end side in the unit housing, i.e., with the inner peripheral portion of the side opposite the cross roller bearing. An outer race of the cross roller bearing is secured to the unit housing, and an inner race thereof is secured to a boss of the externally toothed gear. The two gears are supported by the cross roller bearing so as to be capable of relative rotation.